From ac85bea5218a10a1b733de9d8c7e8880fd7258ae Mon Sep 17 00:00:00 2001 From: guyotv Date: Sun, 11 Sep 2022 22:16:06 +0200 Subject: [PATCH] Deux premiers exos d'incertitudes. --- Annexe-Exercices/Annexe-Exercices.tex | 44 +++++++++++++++++- Annexe-Exercices/Annexe-Exercices.tex.bak | 44 +++++++++++++++++- Annexe-Incertitudes/Annexe-Incertitudes.tex | 2 +- .../Annexe-Incertitudes.tex.bak | 12 ++--- CoursMecaniqueOSDF.pdf | Bin 12827241 -> 12831037 bytes SolutionsOS.tex | 26 +++++++++++ 6 files changed, 119 insertions(+), 9 deletions(-) diff --git a/Annexe-Exercices/Annexe-Exercices.tex b/Annexe-Exercices/Annexe-Exercices.tex index 5a93024..4eb0321 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex +++ b/Annexe-Exercices/Annexe-Exercices.tex @@ -2525,7 +2525,49 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r \[c_?=\frac{1295,8}{2,92}=\SI{444}{\joule\celsius\per\kilo\gram}\] En consultant le tableau \ref{tabchaleurmassique}, page \pageref{tabchaleurmassique}, on constate qu'il s'agit de fer. \end{solos} - +\end{exos} +} + +\subsection{Relatifs aux incertitudes} + +\optv{OS}{ + +\begin{exos} + Donnez l'expression de l'incertitude absolue des grandeurs suivantes en fonction des incertitudes absolues des grandeurs mesurées qui permettent de les calculer : + \begin{itemize} + \item L'accélération centripète \[a=\frac{v^2}{R}\] + \item La force de gravitation \[F=G\cdot \frac{M\cdot m}{d^2}\] + \item La position d'un MRUA \[x=\frac{1}{2}\cdot a\cdot t^2 +v_0\cdot t+ x_0\] + \item La vitesse \[v=\frac{x-x_0}{t}\] + \end{itemize} + \begin{solos} + Pour chaque cas, on a~: + \begin{align*} + I(a)&=I(v^2/R)=v^2/R\cdot i(v^2/R)\\ + &=\frac{v^2}{R}\cdot (2\cdot i(v) + i(R))\\ + &=\frac{v^2}{R}\cdot (2\cdot \frac{I(v)}{v} + \frac{I(R)}{R})\\ + I(F)&=I(G\cdot M\cdot m/d^2)\\ + &=G\cdot M\cdot m/d^2\cdot i(G\cdot M\cdot m/d^2)\\ + &=G\cdot \frac{M\cdot m}{d^2}\cdot (i(G)+i(M)+i(m)+2\cdot i(d))\\ + &=G\cdot \frac{M\cdot m}{d^2}\cdot (\frac{I(G)}{G}+\frac{I(M)}{M}+\frac{I(m)}{m}+2\cdot \frac{I(d)}{d})\\ + I(x)&=I(1/2\cdot a\cdot t^2 +v_0\cdot t+ x_0)\\ + &=I(1/2\cdot a\cdot t^2)+I(v_0\cdot t)+I(x_0)\\ + &=\frac{1}{2}\cdot a\cdot t^2\cdot (i(1/2)+i(a)+2\cdot i(t))\\ + &+v_0\cdot t\cdot (i(v_0)+i(t))+I(x_0)\\ + &=\frac{1}{2}\cdot a\cdot t^2\cdot (0+\frac{I(a)}{a}+2\cdot \frac{I(t)}{t})\\ + &+v_0\cdot t\cdot (\frac{I(v_0}{v_0}+\frac{I(t)}{t})+I(x_0))\\ + I(v)&=I((x-x_0)/t)=\frac{x-x_0}{t}\cdot (i(x-x_0)+i(t))\\ + &=\frac{x-x_0}{t}\cdot (\frac{I(x-x_0)}{x-x_0}+\frac{I(t)}{t})\\ + &=\frac{x-x_0}{t}\cdot (\frac{I(x)+I(x_0)}{x-x_0}+\frac{I(t)}{t}) + \end{align*} + \end{solos} +\end{exos} + +\begin{exos} + À l'aide des mesures faites sur le pendule simple pour déterminer la dépendance de sa période en fonction des paramètres masse, angle et longueur, faites un graphe de la période par paramètre avec Gnuplot à l'intérieur du modèle \LaTeX{} de TP. Inspirez-vous des graphes présentez dans ce modèle. En déterminant les incertitudes absolues de chaque paramètres, reportez-les sur chacun de vos graphes. + \begin{solos} + \dots + \end{solos} \end{exos} } diff --git a/Annexe-Exercices/Annexe-Exercices.tex.bak b/Annexe-Exercices/Annexe-Exercices.tex.bak index 5a93024..c0d465d 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex.bak +++ b/Annexe-Exercices/Annexe-Exercices.tex.bak @@ -2525,7 +2525,49 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r \[c_?=\frac{1295,8}{2,92}=\SI{444}{\joule\celsius\per\kilo\gram}\] En consultant le tableau \ref{tabchaleurmassique}, page \pageref{tabchaleurmassique}, on constate qu'il s'agit de fer. \end{solos} - +\end{exos} +} + +\subsection{Relatifs aux incertitudes} + +\optv{OS}{ + +\begin{exos} + Donnez l'expression de l'incertitude absolue des grandeurs suivantes en fonction des incertitudes absolues des grandeurs mesurées qui permettent de les calculer : + \begin{itemize} + \item L'accélération centripète \[a=\frac{v^2}{R}\] + \item La force de gravitation \[F=G\cdot \frac{M\cdot m}{d^2}\] + \item La position d'un MRUA \[x=\frac{1}{2}\cdot a\cdot t^2 +v_0\cdot t+ x_0\] + \item La vitesse \[v=\frac{x-x_0}{t}\] + \end{itemize} + \begin{solos} + Pour chaque cas, on a~: + \begin{align*} + I(a)&=I(v^2/R)=v^2/R\cdot i(v^2/R)\\ + &=\frac{v^2}{R}\cdot (2\cdot i(v) + i(R))\\ + &=\frac{v^2}{R}\cdot (2\cdot \frac{I(v)}{v} + \frac{I(R)}{R})\\ + I(F)&=I(G\cdot M\cdot m/d^2)\\ + &=G\cdot M\cdot m/d^2\cdot i(G\cdot M\cdot m/d^2)\\ + &=G\cdot \frac{M\cdot m}{d^2}\cdot (i(G)+i(M)+i(m)+2\cdot i(d))\\ + &=G\cdot \frac{M\cdot m}{d^2}\cdot (\frac{I(G)}{G}+\frac{I(M)}{M}+\frac{I(m)}{m}+2\cdot \frac{I(d)}{d})\\ + I(x)&=I(1/2\cdot a\cdot t^2 +v_0\cdot t+ x_0)\\ + &=I(1/2\cdot a\cdot t^2)+I(v_0\cdot t)+I(x_0)\\ + &=\frac{1}{2}\cdot a\cdot t^2\cdot (i(1/2)+i(a)+2\cdot i(t))\\ + &+v_0\cdot t\cdot (i(v_0)+i(t))+I(x_0)\\ + &=\frac{1}{2}\cdot a\cdot t^2\cdot (0+\frac{I(a)}{a}+2\cdot \frac{I(t)}{t})\\ + &+v_0\cdot t\cdot (\frac{I(v_0}{v_0}+\frac{I(t)}{t})+I(x_0))\\ + I(v)&=I((x-x_0)/t)=\frac{x-x_0}{t}\cdot (i(x-x_0)+i(t))\\ + &=\frac{x-x_0}{t}\cdot (\frac{I(x-x_0)}{x-x_0}+\frac{I(t)}{t})\\ + &=\frac{x-x_0}{t}\cdot (\frac{I(x)+I(x_0)}{x-x_0}+\frac{I(t)}{t}) + \end{align*} + \end{solos} +\end{exos} + +\begin{exos} + À l'aide des mesures faites sur le pendule simple pour déterminer la dépendance de sa période en fonction des paramètres masse, angle et longueur, faites un graphe de la période par paramètre avec Gnuplot à l'intérieur du modèle \latex de TP. Inspirez-vous des graphes présentez dans ce modèle. En déterminant les incertitudes absolues de chaque paramètres, reportez-les sur + \begin{solos} + Un autre corrigé de test. + \end{solos} \end{exos} } diff --git a/Annexe-Incertitudes/Annexe-Incertitudes.tex b/Annexe-Incertitudes/Annexe-Incertitudes.tex index e1f7a20..a0de073 100644 --- a/Annexe-Incertitudes/Annexe-Incertitudes.tex +++ b/Annexe-Incertitudes/Annexe-Incertitudes.tex @@ -403,4 +403,4 @@ Ainsi, en imaginant des mesures de temps et de position pour une chute libre, r Si une courbe théorique réalise une prédiction de ces valeurs, on comprend bien qu'elle doit passer par chaque zone rectangulaire formée par les incertitudes, alors qu'elle peut ne pas passer par chaque points, pour être validée par les mesures. \medskip -Il est donc fondamental de représenter l'ensemble des valeurs reportés graphiquement avec leurs barres d'incertitudes. \ No newline at end of file +Il est donc fondamental de représenter l'ensemble des valeurs reportés graphiquement avec leurs barres d'incertitudes. diff --git a/Annexe-Incertitudes/Annexe-Incertitudes.tex.bak b/Annexe-Incertitudes/Annexe-Incertitudes.tex.bak index 312fd3b..a0de073 100644 --- a/Annexe-Incertitudes/Annexe-Incertitudes.tex.bak +++ b/Annexe-Incertitudes/Annexe-Incertitudes.tex.bak @@ -391,6 +391,12 @@ Non seulement la représentation des nombres est affectée par les incertitudes \[A_{grandeur}=A_{mesure}\pm I(A)\] mais l'incertitude apparaît aussi dans la représentation graphique des mesures. +\begin{figure} +\centering +\caption{Barres d'incertitudes\label{explegraphemruaincertitudes}} +\includegraphics{ExpleGraphe.eps} +\end{figure} + \medskip Ainsi, en imaginant des mesures de temps et de position pour une chute libre, réalisées respectivement avec une incertitude sur le temps d'un centième de seconde et sur la position d'un milimètre, on peut représenter celles-ci sous forme graphique en utilisant des \og barres d'incertitudes \fg{}. Le graphe \ref{explegraphemruaincertitudes} présente celles-ci, visibles pour chaque mesures, sous la forme de barres verticales et horizontales entourant les points. À droite et en haut du point sont reportés les valeurs positives de l'incertitude et à gauche et en bas, les valeurs négatives. @@ -398,9 +404,3 @@ Si une courbe théorique réalise une prédiction de ces valeurs, on comprend bi \medskip Il est donc fondamental de représenter l'ensemble des valeurs reportés graphiquement avec leurs barres d'incertitudes. - -\begin{figure}[t] -\centering -\caption{Barres d'incertitudes\label{explegraphemruaincertitudes}} -\includegraphics{ExpleGraphe.eps} -\end{figure} \ No newline at end of file diff --git a/CoursMecaniqueOSDF.pdf b/CoursMecaniqueOSDF.pdf index 7f6c57ac81e0626037db45e4f0cccce49f9e8577..6b4c4e5fe1efa65e7616c8e72c86f19de6e5ad98 100644 GIT binary patch delta 44547 zcmZtN1yEc~_aOY>?ykXt%i!(=cXxMp0t5zkcZZsYNtopdePQxO8Qa9kR~95 z>w>#8t?fD|-DDqIxQn#Y{X=#60LoPqa{vb3^>OV~CB2d&Og!kFx3f$B;ewm&V$S2+ zGPuTY;_&&;>0Qj6)xnvt7Rvz|izQl~ET`9i&9}Yh?RFhEq-+McuO;@5A>>(;EMUWl zS3?8FDzY>JJ->SN5cW}vJLkGx3FlskyFt^Dhy?ZH<7rbm=wP{uN!%#q!K%vxjxSY@ 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